The 41st prime p, for which p^2 - p + 1
is also prime: 2113^2 - 2113 + 1 = 4462657 which is prime,
note that 41 is also prime.

The smallest 4 digit
prime and the 7th prime of the form pi(p)+p: 1831 is prime,
and 2113 = (1831) + 1831.

2113, when written in base 5/2,
is prime: 2*(5/2)^3 + 1*(5/2)^2 + 1*(5/2) + 3 = 43 is
prime; There are 2113 different ways (permutations) of
achieving the score of 24 under American football rules.

The 43rd prime of the form ((p)), where p-2 and
p are twin primes: 205661 and 205663 are twin primes, and
2113 = ((205663)).

The sum of the 35 primes <= 2113 == the sum of the 31 primes > 2113: 1867+1871+...+2111+2113 = 2129+2131+...+2351+2357.

The smallest prime with an equal number of even and odd prime digits that is also the reverse concatenation of two consecutive Fibonacci numbers:
2113 has 1 even prime digit, 1 odd prime digit, and is the
reverse concatenation of two consecutive Fibonacci numbers:
21 and 13. [Noll]

The year 2113 is encoded from Deuteronomy 29:24 to
Deuteronomy 33:14 according to The Bible Code by Michael
Drosnin.

(There are 2 curios for this number that have not yet been approved by an editor.)